This work proposes OM-GRPO, a label-free RLVR framework that decouples reward estimation from policy optimization and introduces Contrast-Augmented Reward, which refines reward estimation via low-cost pairwise comparisons over existing trajectories without additional rollouts.
Abstract
Reinforcement Learning with Verifiable Rewards (RLVR) improves LLM reasoning but typically relies on ground-truth (GT) answers, limiting scalability. Voting-based label-free RLVR replace gold supervision with answer-level consensus from model samples. However, collapse arises when the same answer-level signal is used both to estimate rewards and to drive token-level policy optimization, encouraging the model to directly reinforce answer tokens rather than improve reasoning. We propose OM-GRPO, a label-free RLVR framework that decouples reward estimation from policy optimization. OM-GRPO masks gradients on the answer span while retaining answer-level rewards through a soft consensus signal, shifting optimization pressure away from answer tokens. We further introduce Contrast-Augmented Reward, which refines reward estimation via low-cost pairwise comparisons over existing trajectories without additional rollouts. Across diverse reasoning benchmarks and three LLM backbones, OM-GRPO consistently outperforms existing label-free RLVR methods and matches supervised GT-reward training with stable optimization. This stability is particularly beneficial in the Test-Time Training setting, where OM-GRPO surpasses majority voting by 4.24 points.
Reinforcement learning from verifiable rewards (RLVR) drives chain-of-thought reasoning in large language models, yet its binary outcome reward cannot distinguish among correct trajectories. Existing dense reward alternatives, from surface heuristics to process reward models, either ignore the expert solutions already present in training corpora or require expensive offline annotation. We propose Gradient-Aligned Reward (GAR), which operates in the policy's own gradient space: truncated backpropagation through the output projection layer extracts a compact gradient vector for each rollout, and cosine similarity with an expert-anchor gradient yields a dense, reasoning-aware reward with less than 9% wall-clock overhead. We prove that this cosine admits a multiplicative decomposition into prediction-error and activation-pattern factors, providing a concrete characterization of what the alignment signal measures. On Qwen3-4B and Qwen3-8B, GAR consistently improves over GRPO and other baselines on competition-level math benchmarks and transfers to GPQA Diamond and MMLU-Pro without domain-specific data. Code and data are available at https://github.com/LQgdwind/GAR.
Le-Qi Zheng, Jin-Bo Su, Fang Niu et al.· 2 citations
Test-time reinforcement learning (TTRL) enables models to improve their reasoning without relying on labeled training data, but existing approaches typically optimize a large fraction of the model parameters. This raises a natural question: can effective test-time adaptation emerge when both the reward signal and the optimization space are severely restricted? We answer this question with label-free bias-only TTRL, which uses majority-vote pseudo-labels as rewards and optimizes only approximately 100K bias parameters while keeping the pretrained backbone frozen. On MATH-500, our approach reaches 76.67% accuracy, slightly exceeding our own labeled bias-steering reproduction while optimizing 76,000x fewer parameters than full-parameter TTRL. The same training procedure improves performance across vision-language and audio reasoning tasks, including MathVista, AI2D, LogicVista, and MMAU. We further show that the learned steering vectors transfer to 4,500 held-out MATH problems, indicating that the adaptation is not limited to the problems used during test-time optimization. Finally, we analyze why this highly restricted adaptation can work, showing that majority-vote reliability improves with rollout consensus and that bias subspaces with greater accessible gradient energy exhibit stronger downstream trainability. These results demonstrate that substantial test-time adaptation can emerge from optimizing a tiny bias-only subspace using entirely label-free rewards.
Reinforcement learning with verifiable rewards (RLVR) and on-policy distillation (OPD) have emerged as two dominant methods for post-training reasoning LLMs. Prior work uses OPD's dense token-level supervision to complement the sparse RL reward, fusing the two signals within a single step: either as a \emph{weighted-additive combination} or a \emph{teacher-modulated rescaling} of the RL advantage. In this paper, we show that a simple two-stage scheme, OPD-then-RL, consistently outperforms pure OPD, pure RLVR, and all such joint baselines across logic and math reasoning benchmarks. Beyond the empirical results, we further provide a systematic understanding of this through pass@$k$ behavior, learning dynamics, and parameter updates, yielding a consistent explanation: OPD expands the student's coverage of teacher-supported solutions and RL sharpens within that support, while jointly optimizing the two signals causes them to interfere. To provide a practical recipe, we find that the OPD validation score is the key signal for when to switch to RL, and that OPD is a better cold start for RL than SFT. Together, our results establish OPD-then-RL as a simple yet strong way to combine the two methods, turning two entangled signals into complementary stages.
Bo-Yang Li, Bingsen Chen, Cheng-Hao Yang et al.· 1 citation
Reinforcement learning (RL) has become one of the primary paradigms for reasoning enhancement of large language models (LLMs). In particular, Group Relative Policy Optimization (GRPO) and related algorithms have demonstrated strong performance with outcome-level rewards. However, these methods depend solely on the final answer, without feedback regarding which intermediate steps contribute to success or failure. As task complexity and reasoning trajectory length increase, such sparse final-answer rewards become increasingly insufficient. To address this limitation, we introduce ConsensusBench, a novel dataset designed to provide rule-based process-level signals. We posit that a correct final answer relies on a small set of intermediate conclusions throughout the reasoning process, which can be seen as a verifiable sub-outcome. We identify these sub-outcomes by filtering correct trajectories from N rollouts and clustering semantically equivalent intermediate statements. We call these clustered statements as Consensus Nodes. By integrating a rule-based process reward derived from these nodes into GRPO-style algorithms, we develop a new reinforcement learning signal named ConsensusPR. It directly reduces the reward sparsity of outcome reward across long reasoning trajectories. To facilitate systematic process-level evaluation, we introduce three metrics to our benchmark: Final Answer Accuracy (Acc), Node Coverage Rate (NCR), and Tokens per Node (TPN). Experiments across AIME 2024, AIME 2025, GSM8K, MATH-500, and our ConsensusBench demonstrate that the proposed method consistently surpasses GRPO-style approaches, highlighting the practical value of consensus nodes in guiding reasoning.
Shi-Qi Yan, Chao-Hong Tan, Qian Chen et al.· 0 citations
On unlabeled test data, reinforcement learning lacks a ground-truth reward; test-time RL methods derive one from the model's own roll-outs, rewarding those that match the majority vote over $N$ sampled answers. That vote discards a correct answer whenever it is a minority and scores every majority-matching roll-out identically. We replace it with \emph{CoRE} (Consensus Rewards via Equilibrium): the $N$ roll-outs form a graph whose edges combine answer agreement, reasoning similarity, and generation confidence, and replicator dynamics extract its dominant set, yielding a refined pseudo-label, a graded per-roll-out reward, and a per-question cohesiveness gate. CoRE strictly generalizes voting: majority voting is recovered as a special case; a block-value analysis gives a sharp threshold for when consensus recovers a correct minority against a larger wrong plurality; and confidence calibration provably lowers that threshold multiplicatively. Across seven backbones and five benchmarks (42 model--benchmark cells, three seeds each), \emph{CoRE} improves the untrained base by $+21.7$ points on average versus $+20.4$ for majority-vote TTRL, wins wherever agreement is contestable with margins over the vote of up to $+7.5$ points, and reaches the voting baseline's plateau accuracy in $54$--$70$\% fewer steps. Consensus, not counting: treating the roll-out group as a graph rather than a ballot box turns a brittle vote into a calibrated, graded, self-supervised reward at no extra roll-out cost.
Test-time reinforcement learning adapts a model on its own unlabeled test set using majority-vote pseudo-labels and has shown strong results in mathematics. We show that this recipe collapses on medical multiple-choice QA: accuracy stagnates while output diversity rapidly declines. Through a controlled experiment that keeps the questions, model, and optimizer fixed while changing only the answer space, we trace this failure to answer-space structure rather than domain difficulty. In small answer spaces, incorrect rollouts often collide on the same wrong pseudo-label and reinforce it; in large answer spaces, they disperse and receive little reward. This diagnosis motivates PROSE, Process Reward Guided Self-Training, which rewards reasoning quality instead of answer agreement. PROSE scores each reasoning step with a medical process reward model, assigns the trajectory reward as the minimum score across steps, and enforces answer-format constraints. Without labels, PROSE substantially improves a general Llama model, surpassing purpose-built medical models and matching much larger systems. Because the process signal is internalized into the policy, the adapted model requires no reward model at inference and transfers its gains to unseen datasets. We further show that the minimum aggregation is essential: mean aggregation can be exploited, saturating the proxy reward while degrading accuracy.
Kai-Long Fan, An-Qi Pu, Yi-Chen Wu et al.· 0 citations
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